12.5 hp Briggs and stratton lawn mower and when it gets hot it cuts off why is that?

Three things come to mind:

1) The cooling fins that keep the engine cool are blocked by debris and letting the mower run hot.

2) The coil is getting hot and breaking down causing it to not get spark to the engine.

3) There might be an exhaus leak near the carb causing the gas to vapor lock.